Logan and Maisie are stood on
opposite sides of a phone mast. The
phone mast is 120 m tall.
The angle of elevation from Logan to
the top of the mast is .
The angle of elevation from Maisie tc
the top of the mast is .

To find the distances from Logan and Maisie to the phone mast, we can apply some trigonometry! For Logan, using the angle of elevation of and the height of the mast (120 m), we can use the tangent function:

where is Logan’s distance from the base of the mast. Rearranging gives us . For Maisie, we do the same using for her distance calculation.

Now, knowing this allows us to visualize the scenario better. Imagine a triangle where you can see how the height of the mast creates a perfect contrast against the angles.

When it comes to real-world application, this type of problem can be seen in fields like architecture or telecommunications, where understanding the heights and distances of structures is crucial. Engineers often need to calculate angles of isolation and interference in buildings or towers to optimize signal coverage and construction design, ensuring there aren’t any unexpected blind spots!